1885.] 



Note on a 'previous Paper. 



323 



Part I, 1882, p. 187) lias been found to be erroneous in certain points. 

 The errors, however, do not touch the physical conclusions there 

 attained. As this note has importance only in connexion with' the 

 paper, I proceed in the form of an appendix, without explanation of 

 the notation. 



In the first place — 



Throughout the paper the normal stresses P, Q, R require an addi- 

 tional term Wi. The only function of these stresses used in obtaining 

 physical results is P— R, and it remains unchanged when this correc- 

 tion is made. 



The error takes its origin in § 1. Thomson's solution (1) when 

 reduced to the form applicable to the incompressible solid, is the solu- 

 tion of the equations -y+i>V 2 *=^ and two others. The solution 



dx dx 



required is that of — ^-ffV 2 «=0, and two others. The IF involved 



(XX 



in my solution is not the potential of a true bodily force, but only an 

 " effective potential " producing the same strains as those due to the 

 weight of the continents and mountains, but causing a different 

 hydrostatic pressure. When, therefore, p is determined from Thom- 

 son's solution, that p is really equal to p + Wi of the problem of the 



continents. Hence equation (3) should be p= ~^1 + ~y)^> instead 



of p= — ~Wi. The correction to (3) must be carried on through the 



rest of the paper, and obviously it merely adds Wi to the stresses 

 P, Q, R, leaving P — R, P — Q, Q— R unchanged. 



The error would have been avoided had I, as suggested on p. 190, 

 worked directly fiom the equations of equilibrium of the elastic in- 

 compressible solid, instead of from Thomson's solution. 



When the solid is compressible, this method of " effective poten- 

 tial " (see " The Tides of a Viscous Spheroid," " Phil. Trans.," Part I, 

 1879, pp. 7-9) for including all the effects of gravitation is not appli- 

 cable without certain additional terms in «, /3, 7. Hence in § 10 where 

 the solid is treated as being compressible the expressions for the 

 stresses are incomplete. It will be found, however, that this incom- 

 pleteness does not extend to the case of the mountains and valleys on 

 the mean level surface, and that portion of the section remains cor- 

 rect. It would not be difficult to make the requisite corrections to 

 the earlier part of the section, but I do not think it Avorth while to 

 do so. 



In the second place — 



On p. 191 the following passage occurs : — 



" It may be seen from considerations of symmetry that if Wi be a 

 zonal harmonic, two of the principal stress-axes lie in a meridional 



